Question

it's a two mark question.... Please answer with correct explanation​

Answer 1

Step-by-step explanation:

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I am basic maths student

Answer 2

Answer:

To Prove:

• $\sf{\dfrac{2\cos^{2}\theta-1}{\sin\theta \cos\theta}=\cot\theta-\tan\theta}$

✺Solution✺

We should know following things before solving the question:

$\rightarrow\sf{\cos2\theta=2\cos^{2}\theta-1= \cos^{2}\theta-\sin^{2}\theta }$

$\rightarrow\sf{\dfrac{a-b}{c}=\dfrac{a}{c}-\dfrac{b}{c}}$

$\rightarrow\sf{\dfrac{\cos\theta}{\sin\theta}=\cot\theta}$

$\rightarrow\sf{\dfrac{\sin\theta}{\cos\theta}=\tan\theta}$

Now, using above identities, we get

L.H.S.=$\sf{\dfrac{2\cos^{2}\theta-1}{\sin\theta \cos\theta}}$

$\implies\sf{\dfrac{\cos2\theta}{\sin\theta \cos\theta}}$

$\implies\sf{\dfrac{\cos^{2}\theta-\sin^{2}\theta}{\sin\theta \cos\theta}}$

$\implies\sf{\dfrac{\cos^{2}\theta}{\sin\theta \cos\theta}-\dfrac{\ sin^{2}\theta}{\sin\theta \cos\theta}}$

$\implies\sf{\dfrac{\cos\theta}{\sin\theta}-\dfrac{\ sin\theta}{\cos\theta}}$

$\implies\sf{\cot\theta-\tan\theta}$

$\implies\sf{R.H.S.}$

Since, L.H.S.=R.H.S.

Hence Proved